Mole (unit)

In chemistry and physics, the mole is an SI base unit of amount of substance. Mole is the amount and mol (without an ending e) is the corresponding unit. The word "mole" is shortened from "gram molecular weight", the original term. Industrial chemists also used a "kilogram molecular weight", equal to 1 Kmole.

Loosely speaking, the mole may be defined for a pure substance, consisting of one kind of molecules, as the amount of substance that weighs in grams as much as the molecular weight of the molecule. For instance, one mole of pure water (H₂O, molecular weight of the molecule is 18.02) is the amount of water that weighs 18.02 gram. That is, one mole of water is about 18 mliter at ambient temperature and pressure.

This definition is somewhat loose in the sense that the verb "weighs" is nowadays replaced by "has mass". Further the term "molecular weight" is being phased out and replaced by relative molecular mass. And, also, the definition given here is too restricted. The definition can—and must—be extended to different entities: molecules, ions, atoms, electrons, etc.

A more modern definition of the mole relies on Avogadro's constant N_A (≈ 6×10²³/mol). It reads: a mole consists of N_A entities.

The total mass of an amount of substance is the sum of the masses of its entities. For example, consider a pure substance B of entities with molecular mass M(B) u ( u is unified atomic mass unit). Recalling that

1 u = 1/N_A gram,

we find that one mole of B weighs N_A × M(B) u = M(B) gram. For example, N_A molecules of water (B = H₂O) have mass 18.02 gram.

Let us give another example. The standard atomic weight of magnesium M(Mg) = 24.3050 u, which is the mass of a magnesium atom averaged over its isotopes weighted by natural abundance. One mole of magnesium is N_A × M(Mg) u = 24.3050 10⁻³ kg. This example shows that the atomic mass of any element can be interpreted in two ways: (1) the average mass of a single atom in unified atomic mass units (u) or (2) the average mass of a mole of atoms in grams. For magnesium, (1) the average mass of a single magnesium atom is 24.3050 u or (2) the average mass of a mole of magnesium atoms is 24.3050 gram.

Futher examples: a mole of hydrogen molecule, standard atomic weight of H is 1.00794, has the mass 2×1.00794 = 2.01588 ⁻³ kg. A mole of oxygen, standard atomic weight 15.9994, has the mass 31.9988 10⁻³ kg.

One can include the definition of Avogadro's number in the definition of mole and replace gram by the SI unit kilogram. This leads to the following rather technical definition, which is independent of the definition of Avogadro's number. This is the SI definition, which reads: the mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of ¹²C (carbon-12).

One mole of an ideal gas occupies 22.414 litres at "standard temperature and pressure" (273.15K = 0 ⁰C and 101.325 kPa = 1 atm).

To explain the usefulness of the mole concept we consider the following example of a chemical reaction:

2 A + 6 B → 2 AB₃

This equation is expressed in numbers of atoms and molecules, which are impractical to measure or count directly. However, if we multiply the equation by Avogodro's number, it is expressed in macroscopic quantities. The equation tells us then that 2 moles of A react with 6 moles of B to give 2 moles of AB₃.

In general, the molecular masses of the compounds A [ = M(A)] and B [ = M(B)] are known and hence also is the molecular mass of AB₃ [ = M(AB₃)]. The reaction equation can be translated thus: 2M(A) gram of A reacts with 6M(B) gram of B to give 2M(AB₃) gram of AB₃.

A real life example:

2H₂ + O₂ → 2H₂O

Using rounded numbers: 4 gram H₂ reacts with 32 gram O₂ giving 36 gram H₂O.

Notes

Sources

• mole. Sizes.com (2006-11-07). Retrieved on 2007-05-11.